Understanding Poker Probability

A good poker player acknowledges the fact that the law of probability in poker is essential. A poker player should be able to make some judgment as to what his chances are of making up a particular hand. If a player has drawn a flush, it will help him immensely if he knows the probability that his opponent has of putting together a superior hand. In poker, the probability of occurrence of certain events can also be calculated mathematically.

While calculating the probability of a card game, there are basically two approaches. The first one is to find out the number of outcomes which are likely to satisfy the condition that is being evaluated and then divide it by total number of possible outcomes. For example, for a pair of aces in Texas Hold'em, there are six likely outcomes and they are (Club A, Hearts A), (Spade A, Diamond A), (Spade A, Club A), (Hearts A, Diamond A), (Hearts A, Spade A) and (Diamond A, Club A). There are 52 different ways to select the first card and 51 ways to select the second card. Also, there are two ways to pick the two cards which gives (52/51)/2=1326 likely outcomes dealing with two cards. So, the probability of occurrence of two aces is 6/1326=1/221.

The second approach is by using conditional probability and in complex situation a decision tree. For example, there are four ways to pick an ace out of choices of 52 for the first card to result in a probability of 4/52=1/13. There are three ways to get dealt an ace out of 51 choices on the second card after dealing an ace on the first card for a probability of 3/51=1/17. The conditional probability of being dealt two aces is product of two probabilities: 1/13x 1/17=1/221.

The main trick to determine probability is to select the best approach to a given problem. There is no doubt that this all sounds very complicated and most of the mathematics involved is beyond an average player’s ability to grasp immediately. The situation is worsened by non-availability of calculator on hand and pressure applied by opponents to put up or close. So, the best way to simplify this is to familiarize with various hands and then devise strategy taking into account the probability involved in these hands. The various hands are Royal Flush, Four of a Kind, Straight Flush, Flush, Full House, Straight, Three of a Kind, One Pair, Two Pair and High Card.

Then there are poker odds which can be predicted using probability formulae. The various odds that are likely to arise are simple poker odds, Texas Hold'em odds, Pre-Flop odds, Flop odds, Turn and River Odds, etc.

There are poker calculators available which can do these calculations for the player and make understanding of poker probability easier.

All said and done, the fact is that majority of poker players try little to no calculations amidst a hand. Calculations seem fine between games to checkout probability, but while taking practical decision, it is believed that our brain prefers the simplest rules instead of performing sophisticated calculations. Very few poker players reason with number and midst of pot, a player is most unlikely to work with numbers and instead may opt for common sense approach.

Reversed Probability

Reversed probability is very basis for the theory of probability which deals with decisions and reasoning. Suppose your opponent raises on flop, does this action give any indication about his weak or strong hand. To simply, ask this question in reverse: What is the likelihood of him raising if he owns a weak hand and how likely he will raise if he has strong hand?

Here you do not need numbers, just comparison of two uncertain events or opinion on them. If there is strong likelihood of him raising with strong hand rather than with weak hand, then most probably he has a strong hand.

That is how reversed probability functions. Nothing is said with certainty, but it makes our mind to think in that direction. So, probability is not only about numbers. When a player is in a hand, he is more unlikely to see a figure of 52 or 62. His mind will be working on what his opponent has in a tight situation. In the same way, other factors can also be brought into picture such as interpretation of opponent's behavior, his reaction, and other such hypotheses.

Thus, probability in poker gives you some chance of predicting the outcome of a move or a hand and it need not always be mathematical in nature.

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